I don't know what sort of stuff you like, but holy shit
Westminster Abbey impressed the hell out of me. I love massive churches/cathedrals though, all that stained glass, the architecture and just knowing that it's sooooo damn old.
Of course it's right by the London Eye, Big Ben and the Parliament buildings which are all worth a look as well, so that helps. Taking a ride on the London Eye in the evening is fantastic, you can see for miles and the city looks fantastic at night. I think you'd want to book that in advance as it can be quite busy.
We love a bus tour early in the visit because it orients you to the city and you get some ideas of what you'd like to see. I can recommend
these guys they have a few (3?) different routes that you can take all for one price. The ticket is good for 24 hours and is hop-on-hop-off wherever you like so it's a great way to get around the city cheap as well. You can get a 48 hour ticket too. Plus the ticket includes a free river cruise on the Thames and some other stuff. Try to get one of the buses that have a live tour guide (rather than the earphones ones) because they really add a lot to the tour, giving great background info as you go.
Those are sort of the really obvious things, so no surprises there.
I would also recommend the Science Museum and the Natural History Museum if you like that sort of thing, but be aware that they are HUGE and could easily take an entire day each if you're thorough. On the other hand, my dad and I sort of breezed through the Science Museum just cherry picking things that looked up our alley and did it in about 2 hours.
Finally, I would also recommend a Jack The Ripper Tour. They're walking tours that take about 2 hours. Again, nice info about the city during that era and just a fun way to go over the Ripper case.